Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.1.77-90
V. I. Pan’zhenskii, B. A. Rastrepina
Among the known eight-dimensional Thurston geometries, there is a geometry of the Sol manifold – a Lie group consisting of real special matrices. For a left-invariant Riemannian metric on the Sol manifold, the left shift group is a maximal simple transitive group of isometry. In this paper, we found all left-invariant differential 1-forms and proved that on the oriented Sol manifold there is only one left-invariant differential 1-form, such that this form and the left-invariant Riemannian metric together define the contact metric structure on the Sol manifold. We identified all left-invariant contact metric connections and distinguished flat connections among them. A completely non-holonomic contact distribution along with the restriction of a Riemannian metric to this distribution define the contact metric structure on the Sol manifold, and an orthogonal projection of the Levi-Chivita connection is a truncated connection. We obtained geodesic parameter equations of the truncated connection, which are the sub-geodesic equations, using a non-holonomic field of frames adapted to the contact metric structure. We revealed that these geodesics are a part of the geodesics of the flat contact metric connection.
{"title":"The Left-Invariant Contact Metric Structure on the Sol Manifold","authors":"V. I. Pan’zhenskii, B. A. Rastrepina","doi":"10.26907/2541-7746.2020.1.77-90","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.1.77-90","url":null,"abstract":"Among the known eight-dimensional Thurston geometries, there is a geometry of the Sol manifold – a Lie group consisting of real special matrices. For a left-invariant Riemannian metric on the Sol manifold, the left shift group is a maximal simple transitive group of isometry. In this paper, we found all left-invariant differential 1-forms and proved that on the oriented Sol manifold there is only one left-invariant differential 1-form, such that this form and the left-invariant Riemannian metric together define the contact metric structure on the Sol manifold. We identified all left-invariant contact metric connections and distinguished flat connections among them. A completely non-holonomic contact distribution along with the restriction of a Riemannian metric to this distribution define the contact metric structure on the Sol manifold, and an orthogonal projection of the Levi-Chivita connection is a truncated connection. We obtained geodesic parameter equations of the truncated connection, which are the sub-geodesic equations, using a non-holonomic field of frames adapted to the contact metric structure. We revealed that these geodesics are a part of the geodesics of the flat contact metric connection.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"51 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86017513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.4.387-395
S. Selezneva
{"title":"On the Chromatic Number of Graphs with Some Restriction of Vertex Degrees","authors":"S. Selezneva","doi":"10.26907/2541-7746.2020.4.387-395","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.4.387-395","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"17 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78724340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.2.180-192
K. Potashev, R. Akhunov
Estimation of the heterogeneity of the reservoir fluid inflow to the cross-sectional contour of a vertical well. Russian) Abstract The reasons for the heterogeneity of the reservoir fluid inflow to the cross-sectional contour of a vertical well can be: a) asymmetry of the external pressure field relative to the well axis as a result of the interference of the surrounding wells; b) heterogeneity of the permeability field near the well, which is a consequence of either the heterogeneity of the absolute permeability field of the reservoir or the mobility function of the multiphase mixture of formation fluids. To simulate filtration in a reservoir over a relatively long time interval, the main interest is constant or long-term factors associated with well spacing and the distribution of absolute permeability. In the work, solutions of two model problems were constructed, which allow a quantitative evaluation of the influence of both factors on the degree of inhomogeneity of the inflow to the well and indicate the conditions under which this effect becomes significant. The obtained estimates are intended primarily for computational schemes of streamline and streamtube methods, which require a high degree of solution detailing near wells.
{"title":"Estimation of the Heterogeneity of the Reservoir Fluid Inflow to the Cross-Sectional Contour of a Vertical Well","authors":"K. Potashev, R. Akhunov","doi":"10.26907/2541-7746.2020.2.180-192","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.2.180-192","url":null,"abstract":"Estimation of the heterogeneity of the reservoir fluid inflow to the cross-sectional contour of a vertical well. Russian) Abstract The reasons for the heterogeneity of the reservoir fluid inflow to the cross-sectional contour of a vertical well can be: a) asymmetry of the external pressure field relative to the well axis as a result of the interference of the surrounding wells; b) heterogeneity of the permeability field near the well, which is a consequence of either the heterogeneity of the absolute permeability field of the reservoir or the mobility function of the multiphase mixture of formation fluids. To simulate filtration in a reservoir over a relatively long time interval, the main interest is constant or long-term factors associated with well spacing and the distribution of absolute permeability. In the work, solutions of two model problems were constructed, which allow a quantitative evaluation of the influence of both factors on the degree of inhomogeneity of the inflow to the well and indicate the conditions under which this effect becomes significant. The obtained estimates are intended primarily for computational schemes of streamline and streamtube methods, which require a high degree of solution detailing near wells.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"39 2 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82831873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.4.411-425
Yu. V. Zuev
Conditions for applying a simplified single-speed and one-temperature (one-liquid) mathematical model, which makes it possible to determine the mean mass speeds and temperatures of the heterogeneous mixture, to calculate the two-phase turbulent non-isothermal jet were defined. Numerical modeling with use of the developed multi-liquid mathematical model of the two-phase jet, in which the speed and temperature of particles differ from the speed and temperature of the gas phase, was carried out. The problem under consideration is extremely important, because two-phase jet parameters are needed to solve numerous applied tasks in va-rious technical areas. These parameters can be accurately determined with the help of simple mathematical models. Based on the resulting calculations carried out with the developed multi-liquid mathematical model of the two-phase turbulent jet, criterial dependences for as-sessing the maximum error of the calculation of two-phase jet flow parameters while using the one-liquid model were obtained.
{"title":"Miscalculation of Two-Phase Turbulent Jet Parameters While Using One-Liquid Mathematical Model","authors":"Yu. V. Zuev","doi":"10.26907/2541-7746.2020.4.411-425","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.4.411-425","url":null,"abstract":"Conditions for applying a simplified single-speed and one-temperature (one-liquid) mathematical model, which makes it possible to determine the mean mass speeds and temperatures of the heterogeneous mixture, to calculate the two-phase turbulent non-isothermal jet were defined. Numerical modeling with use of the developed multi-liquid mathematical model of the two-phase jet, in which the speed and temperature of particles differ from the speed and temperature of the gas phase, was carried out. The problem under consideration is extremely important, because two-phase jet parameters are needed to solve numerous applied tasks in va-rious technical areas. These parameters can be accurately determined with the help of simple mathematical models. Based on the resulting calculations carried out with the developed multi-liquid mathematical model of the two-phase turbulent jet, criterial dependences for as-sessing the maximum error of the calculation of two-phase jet flow parameters while using the one-liquid model were obtained.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"12 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87821111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.1.5-26
E. Izotova, M. Rudakova, N. Akberova
In this work, we studied the diversity of silicic acid oligomers with Si n =(3 − 8) obtained during molecular dynamics in a reaction Feston–Garofalini force field that describes the process of oligomerization of silicic acids in an aqueous solution at the atomic level. Two systems with different concentrations of silicic acids, including 576 and 729 monomers Si(OH) 4 , were studied. According to the calculation results, the highest frequency isomers were represented by linear and branched forms. Throughout the simulation, a high level of dimers was constantly observed. The silicic acids oligomers size increased over time up to 27 Si atoms. The distribution of oligomers by the frequency of permeability for Si n =(3 − 5) was almost completely comparable with the NMR 29Si and quantum-chemical calculations. A previously undescribed new low-frequency isomer presented in both studied systems was identified among the pentamers. For oligomers with Si n =(6 − 8) , a wide variety of spatial isomers were observed; some of them have been partially or completely detected experimentally. Analysis of the Si average coordination number during MD simulation showed that 98% of Si atoms have a degree of coordination IV.
在这项工作中，我们研究了Si n =(3−8)的硅酸低聚物的多样性，这是在反应feton - garofalini力场的分子动力学中获得的，该力场描述了硅酸在水溶液中的原子水平上的低聚过程。研究了含576和729单体Si(OH) 4的两种不同浓度硅酸体系。根据计算结果，频率最高的异构体由线性和分支形式表示。在整个模拟过程中，不断观察到高水平的二聚体。随着时间的推移，硅酸低聚物的大小增加到27个Si原子。Si n =(3−5)的渗透率频率分布与核磁共振29Si和量子化学计算几乎完全相似。在这两种研究体系中都发现了一种以前描述过的新的低频异构体。对于Si n =(6−8)的低聚物，可以观察到各种不同的空间异构体;其中一些已经部分或完全被实验检测到。MD模拟中对Si平均配位数的分析表明，98%的Si原子具有IV级配位。
{"title":"The Molecular Dynamics of Silica Acids in Aqueous Solution: Qualitative and Quantitative Characteristics of Oligomers","authors":"E. Izotova, M. Rudakova, N. Akberova","doi":"10.26907/2541-7746.2020.1.5-26","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.1.5-26","url":null,"abstract":"In this work, we studied the diversity of silicic acid oligomers with Si n =(3 − 8) obtained during molecular dynamics in a reaction Feston–Garofalini force field that describes the process of oligomerization of silicic acids in an aqueous solution at the atomic level. Two systems with different concentrations of silicic acids, including 576 and 729 monomers Si(OH) 4 , were studied. According to the calculation results, the highest frequency isomers were represented by linear and branched forms. Throughout the simulation, a high level of dimers was constantly observed. The silicic acids oligomers size increased over time up to 27 Si atoms. The distribution of oligomers by the frequency of permeability for Si n =(3 − 5) was almost completely comparable with the NMR 29Si and quantum-chemical calculations. A previously undescribed new low-frequency isomer presented in both studied systems was identified among the pentamers. For oligomers with Si n =(6 − 8) , a wide variety of spatial isomers were observed; some of them have been partially or completely detected experimentally. Analysis of the Si average coordination number during MD simulation showed that 98% of Si atoms have a degree of coordination IV.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"12 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81207811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.1.91-97
R. Salimov, I. Kareev
The standard problem of assessing the proportion of substandard products was considered in the framework of the Bayesian paradigm in the sense of the problem of optimal estimation. This problem was reduced to assessing the probability of success in a binomial scheme with a quadratic loss function for which a prior beta distribution applies. Unlike the classical approach to parameter estimation, we used the d -posterior approach to construct statistical guarantee solutions. Estimates with the uniformly minimal d -risk and the Bayesian estimate are constructed. The last one is necessary for designing a d -guaranteed sequential “first crossing” procedure. The sequential procedure leads to significant reduction of the inspection volume of products batch. In this regard, the task of planning the volume of tests that guarantees a given restriction on d -risk was solved.
{"title":"Binomial Probability Estimates with Restrictions on Their d-Risks","authors":"R. Salimov, I. Kareev","doi":"10.26907/2541-7746.2020.1.91-97","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.1.91-97","url":null,"abstract":"The standard problem of assessing the proportion of substandard products was considered in the framework of the Bayesian paradigm in the sense of the problem of optimal estimation. This problem was reduced to assessing the probability of success in a binomial scheme with a quadratic loss function for which a prior beta distribution applies. Unlike the classical approach to parameter estimation, we used the d -posterior approach to construct statistical guarantee solutions. Estimates with the uniformly minimal d -risk and the Bayesian estimate are constructed. The last one is necessary for designing a d -guaranteed sequential “first crossing” procedure. The sequential procedure leads to significant reduction of the inspection volume of products batch. In this regard, the task of planning the volume of tests that guarantees a given restriction on d -risk was solved.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"52 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85008230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.1.24-38
E. Kronrod, Y. Nefedyev, V. Kronrod, O. Kuskov, A. Andreev
{"title":"Selenophysics and Models of the Lunar Three-Layered Mantle","authors":"E. Kronrod, Y. Nefedyev, V. Kronrod, O. Kuskov, A. Andreev","doi":"10.26907/2541-7746.2019.1.24-38","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.1.24-38","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"3 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88886555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.1.39-52
A. Aganin, T. Guseva
{"title":"The Influence of the End Shape of the Liquid Jet on Its Impact onto a Dry Wall","authors":"A. Aganin, T. Guseva","doi":"10.26907/2541-7746.2019.1.39-52","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.1.39-52","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"8 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85452878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.26907/2541-7746.2019.1.127-144
M. N. Matveev
Simplicial fixed point algorithms can be based on either integer or vector labels. An ap-parent advantage of the algorithms with integer labels is their simplicity and stability under round-off errors due to the discrete nature of integer labels. At the same time, the application of all existing algorithms with integer labels is limited by some rigidness of their construction, in particular, in the d -dimensional space they can bear only from d +1 to 2 d labels. The num-bers of labels comparable with the dimension of space make these algorithms not very fast, especially in high-dimensional tasks. This paper overcomes this rigidness and builds a new simplicial fixed point algorithm with 2 d integer labels. To achieve this goal, the paper proves new properties of triangulation K 1 and separates all approximations of fixed points into weak and strong ones. This separation, which has never been used until this moment, is caused by the high number of labels of the new algorithm.
{"title":"Simplicial Fixed Point Algorithm with 2d Integer Labels","authors":"M. N. Matveev","doi":"10.26907/2541-7746.2019.1.127-144","DOIUrl":"https://doi.org/10.26907/2541-7746.2019.1.127-144","url":null,"abstract":"Simplicial fixed point algorithms can be based on either integer or vector labels. An ap-parent advantage of the algorithms with integer labels is their simplicity and stability under round-off errors due to the discrete nature of integer labels. At the same time, the application of all existing algorithms with integer labels is limited by some rigidness of their construction, in particular, in the d -dimensional space they can bear only from d +1 to 2 d labels. The num-bers of labels comparable with the dimension of space make these algorithms not very fast, especially in high-dimensional tasks. This paper overcomes this rigidness and builds a new simplicial fixed point algorithm with 2 d integer labels. To achieve this goal, the paper proves new properties of triangulation K 1 and separates all approximations of fixed points into weak and strong ones. This separation, which has never been used until this moment, is caused by the high number of labels of the new algorithm.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85664037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：